Set of real numbers: Difference between revisions
→{{header|C sharp}}
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* Define ''[http://www.wolframalpha.com/input/?i=%7Csin%28pi+x2%29%7C%3E1%2F2%2C+0+%3C+x+%3C+10 A]'' = {''x'' | 0 < ''x'' < 10 and |sin(π ''x''²)| > 1/2 }, ''[http://www.wolframalpha.com/input/?i=%7Csin%28pi+x%29%7C%3E1%2F2%2C+0+%3C+x+%3C+10 B]'' = {''x'' | 0 < ''x'' < 10 and |sin(π ''x'')| > 1/2}, calculate the length of the real axis covered by the set ''A'' − ''B''. Note that
|sin(π ''x'')| > 1/2 is the same as ''n'' + 1/6 < ''x'' < ''n'' + 5/6 for all integers ''n''; your program does not need to derive this by itself.
=={{header|cpp}}==
{{trans|Java}}
<lang cpp>#include <cassert>
#include <functional>
#include <iostream>
#define _USE_MATH_DEFINES
#include <math.h>
enum RangeType {
CLOSED,
BOTH_OPEN,
LEFT_OPEN,
RIGHT_OPEN
};
class RealSet {
private:
double low, high;
double interval = 0.00001;
std::function<bool(double)> predicate;
public:
RealSet(double low, double high, const std::function<bool(double)>& predicate) {
this->low = low;
this->high = high;
this->predicate = predicate;
}
RealSet(double start, double end, RangeType rangeType) {
low = start;
high = end;
switch (rangeType) {
case CLOSED:
predicate = [start, end](double d) { return start <= d && d <= end; };
break;
case BOTH_OPEN:
predicate = [start, end](double d) { return start < d && d < end; };
break;
case LEFT_OPEN:
predicate = [start, end](double d) { return start < d && d <= end; };
break;
case RIGHT_OPEN:
predicate = [start, end](double d) { return start <= d && d < end; };
break;
default:
assert(!"Unexpected range type encountered.");
}
}
bool contains(double d) const {
return predicate(d);
}
RealSet unionSet(const RealSet& rhs) const {
double low2 = fmin(low, rhs.low);
double high2 = fmax(high, rhs.high);
return RealSet(
low2, high2,
[this, &rhs](double d) { return predicate(d) || rhs.predicate(d); }
);
}
RealSet intersect(const RealSet& rhs) const {
double low2 = fmin(low, rhs.low);
double high2 = fmax(high, rhs.high);
return RealSet(
low2, high2,
[this, &rhs](double d) { return predicate(d) && rhs.predicate(d); }
);
}
RealSet subtract(const RealSet& rhs) const {
return RealSet(
low, high,
[this, &rhs](double d) { return predicate(d) && !rhs.predicate(d); }
);
}
double length() const {
if (isinf(low) || isinf(high)) return -1.0; // error value
if (high <= low) return 0.0;
double p = low;
int count = 0;
do {
if (predicate(p)) count++;
p += interval;
} while (p < high);
return count * interval;
}
bool empty() const {
if (high == low) {
return !predicate(low);
}
return length() == 0.0;
}
};
int main() {
using namespace std;
RealSet a(0.0, 1.0, LEFT_OPEN);
RealSet b(0.0, 2.0, RIGHT_OPEN);
RealSet c(1.0, 2.0, LEFT_OPEN);
RealSet d(0.0, 3.0, RIGHT_OPEN);
RealSet e(0.0, 1.0, BOTH_OPEN);
RealSet f(0.0, 1.0, CLOSED);
RealSet g(0.0, 0.0, CLOSED);
for (int i = 0; i <= 2; ++i) {
cout << "(0, 1] ∪ [0, 2) contains " << i << " is " << boolalpha << a.unionSet(b).contains(i) << "\n";
cout << "[0, 2) ∩ (1, 2] contains " << i << " is " << boolalpha << b.intersect(c).contains(i) << "\n";
cout << "[0, 3) - (0, 1) contains " << i << " is " << boolalpha << d.subtract(e).contains(i) << "\n";
cout << "[0, 3) - [0, 1] contains " << i << " is " << boolalpha << d.subtract(f).contains(i) << "\n";
cout << endl;
}
cout << "[0, 0] is empty is " << boolalpha << g.empty() << "\n";
cout << endl;
RealSet aa(
0.0, 10.0,
[](double x) { return (0.0 < x && x < 10.0) && abs(sin(M_PI * x * x)) > 0.5; }
);
RealSet bb(
0.0, 10.0,
[](double x) { return (0.0 < x && x < 10.0) && abs(sin(M_PI * x)) > 0.5; }
);
auto cc = aa.subtract(bb);
cout << "Approximate length of A - B is " << cc.length() << endl;
return 0;
}</lang>
{{out}}
<pre>(0, 1] ? [0, 2) contains 0 is true
[0, 2) ? (1, 2] contains 0 is false
[0, 3) - (0, 1) contains 0 is true
[0, 3) - [0, 1] contains 0 is false
(0, 1] ? [0, 2) contains 1 is true
[0, 2) ? (1, 2] contains 1 is false
[0, 3) - (0, 1) contains 1 is true
[0, 3) - [0, 1] contains 1 is false
(0, 1] ? [0, 2) contains 2 is false
[0, 2) ? (1, 2] contains 2 is false
[0, 3) - (0, 1) contains 2 is true
[0, 3) - [0, 1] contains 2 is true
[0, 0] is empty is false
Approximate length of A - B is 2.07587</pre>
=={{header|C sharp}}==
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